I'm learning supersymmetry, supergravity and superstring. I want some problems books to have some idea in this area. Is there this kind of books? Or are there some papers that have many solved model?
For supersymmetry and supergravity, my primary recommendation is
Supergravity by Freedman and Van Proeyen. This book has a very large number of exercises interspersed across the text. The exercises are placed at locations that are relevant to the prose around them, and they vary in their level of difficulty from verifying certain results in the text, to involved problems, so they're well-suited to self-study. As an aside, the prose itself is (at least in the first 10 chapters or so) clear and pedgogical. Although this is not strictly a problem book, it has so many of them that it could effectively function as one for someone who treats it that way. This book will be useful if you have a relatively strong background in QFT and are just getting into research in theoretical high energy.
A secondary recommendation is sections 3.6 and 4.12 of the classic review
"Supersymmetric Gauge Theories and the AdS/CFT Correspondence" by D'Hoker and Freedman. These two sections contain five and four problems respectively on SYM and sugra/superstrings. Although there are not a large number of exercises here, the exercises are interesting and relevant. The level is suitable for anyone with a strong background in QFT and especially the mathematics of symmetry in physics (groups, algebras, etc.)
For Supergravity, my recommendation is, without any doubt, the new edition (2015) of Gravity and Strings by Tomas Ortin. With more than 1000 pages, this book is an impressive piece of work on Gravity, Supergravity and related aspects of String Theory. It is more advanced and more mathematically inclined than "Supergravity" by Freedman and Van Proeyen (another great book). In contrast to the latter, Tomas Ortin adopts a formal geometric approach to Supergravity, describing the mathematical structure of the theory in its final form from the Lorentzian space-time point of view. Tomas Ortin's book focuses on the mathematical formulation of bosonic Supergravity equipped with its Killing spinor equations, exploring it in depth and using it to, for example, classify the local isometry type of all supersymmetric solutions in several low-dimensional supergravities. On the other hand, Freedman and Van Proeyen's book focuses more on how to actually build fully coupled supergravity theories, including its (essentially) complete fermionic sector, explaining the methods that the authors themselves (among others) developed in the 80's to construct supersymmetric theories of gravity (such as the "superconformal formalism").
Tomas Ortin's book contains cutting edge research results on supergravity theories and their solutions: branes, black holes, domain walls... and in fact some of its content regarding the mathematical structures of supergravity cannot be found elsewhere (except a few recent research papers). The book has also various appendices where much of the mathematics used through the text is very well explained in a physics language.
I recommend Tomas Ortin's book to every student that is serious about learning the gravitational aspects of String Theory, in particular Supergravity, as well as to those mathematicians interested in learning about the mathematical (geometric) structures appearing in supergravity and the potential open mathematical problems within these theories. On the other hand, for those interested in learning about how supergravity was actually constructed, I would recommend Freedman and Van Proeyen's book. However, I believe that, from a differential-geometric point of view, one should be perhaps more interested in the mathematical structures appearing in the end supergravity product rather than in the (remarkably complicated) physics methods used to construct it.
-Introduction to Supersymmetry, (Müller-Kirsten, Wiedemann) It's very detailed in every aspect, from graded algebras to the lagrangian of Supersymmetry and symmetry breaking.To be supplemented with something on phenomenology (see below)
-Supersymmetry and Supergravity, (Wess, Bagger) Very advanced, but a bit obscure. To be supplemented by Muller-Wiedemann. It's the standard reference.
-A Supersymmetry Primer, (Martin) Covers the phenomenology and the Supersymmetric-Standard-Model nicely.
String Theory volumes 1 & 2 by Joe Polchinski are very recommendable with many exercises.
See also: Barton Zwiebach: A First Course in String Theory
String Theory and M-Theory: A Modern Introduction, by: J. Schwarz, K. Becker and M. Becker, with many exercises.
Regards. Pascal Kwanten